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411.
This paper models a k-unit service system (e.g., a repair, maintenance, or rental facility) with Poisson arrivals, exponential service times, and no queue. If we denote the number of units that are busy as the state of the system, the state-dependent pricing model formalizes the intuitive notion that when most units are idle, the price (i.e., the service charge per unit time) should be low, and when most units are busy, the price should be higher than the average. A computationally efficient algorithm based on a nonlinear programming formulation of the problem is provided for determination of the optimal state-dependent prices. The procedure ultimately reduces to the search on a single variable in an interval to determine the unique intersection point of a concave increasing function and a linear decreasing function. The algorithm takes, on the average, only about 1/2 second per problem on the IBM 360/65 (FORTRAN G Compiler). A discrete optimal-control approach to the problem is shown to result in essentially the same procedure as the nonlinear-programming formulation. Several properties of the optimal state-dependent prices are given. Comparisons of the optimal values of the objective function for the state-dependent and state-independent pricing policies show that the former is on the average, only about 0.7% better than the latter, which may explain partly why state-dependent pricing is not prevalent in many service systems. Potential generalizations of the model are discussed. 相似文献
412.
This paper shows that by making use of an unusual property of the decision table associated with the dynamic programming solution to the goup problem, it is possible to dispense with table storage as such, and instead overlay values for both the objective and history functions. Furthermore, this storage reduction is accomplished with no loss in computational efficiency. An algorithm is presented which makes use of this technique and incorporates various additional efficiencies. The reduction in storage achieved for problems from the literature is shown. 相似文献
413.
This paper examines problems of sequencing n jobs for processing by a single resource to minimize a function of job completion times, when the availability of the resource varies over time. A number of well-known results for single-machine problems which can be applied with little or no modification to the corresponding variable-resource problems are given. However, it is shown that the problem of minimizing the weighted sum of completion times provides an exception. 相似文献
414.
During basis reinversion of either a product form or elimination form linear programming system, it may become necessary to swap spike columns to effect the reinversion and maintain the desired sparsity characteristics. This note shows that the only spikes which need be examined when an interchange is required are those not yet processed in the current external bump. 相似文献
415.
This paper is concerned with assigning and sequencing a set of activities for some or all members of a crew of operators so that the completion time of all such operations is minimized. It is assumed that each of the operators in the crew possesses, initially, certain tasks that only he can perform. A branch-and-bound scheme is proposed to treat the problem, and suitable computational experience is provided. 相似文献
416.
The problem posed in this paper is to sequence or route n jobs, each originating at a particular location or machine, undergoing r?1 operations or repairs, and terminating at the location or machine from which it originated. The problem is formulated as a 0-1 integer program, with block diagonal structure, comprised of r assignment subproblems; and a joint set of constraints to insure cyclical squences. To obtain integer results the solutions to each subproblem are ranked as required and combinations thereof are implicitly enumerated. The procedure may be terminated at any step to obtain an approximate solution. Some limited computational results are presented. 相似文献
417.
J. L. Brenner 《海军后勤学研究》1969,16(3):359-379
The chief problems considered are: (1) In a parallel set of warehouses, how should stocks be allocated? (2) In a system consisting of a central warehouse and several subsidiary warehouses, how much stock should be carried in each? The demands may have known, or unknown, distribution functions. For problem (1), the i-th stock ni should usually be allocated in proportion to the i-th demand mi; in special cases, a significant improvement is embodied in the formula (N = total allocable stock)
418.
Recent research has led to several surrogate multiplier search procedures for use in a primal branch-and-bound procedure. As single constrained integer programming problems, the surrogate subproblems are also solved via branch-and-bound. This paper develops the inner play between the surrogate subproblem and the primal branch-and-bound trees which can be exploited to produce a number of computational efficiencies. Most important is a restarting procedure which precludes the need to solve numerous surrogate subproblems at each node of a primal branch-and-bound tree. Empirical evidence suggests that this procedure greatly reduces total computation time. 相似文献
419.
This paper investigates the effect on the optimum solution of a capacitated generalized transportation problem when certain data of the problem are continuously varied as a linear function of a single parameter. First the rim conditions, then the cost coefficients, and finally the cell upper bounds are varied parametrically and the effect on the optimal solution, the associated change in costs and the dual changes are derived. Finally the effect of simultaneous changes in both cost coefficients and rim conditions are investigated. Bound operators that effect changes in upper bounds are shown to be equivalent to rim operators. The discussion in this paper is limited to basis preserving operators for which the changes in the data are such that the optimum bases are preserved. 相似文献
420.
This paper investigates the effect on the optimum solution of a capacitated generalized transportation problem when any coefficient of any row constraint is continuously varied as a linear function of a single parameter. The entire analysis is divided into three parts. Results are derived relative to the cases when the coefficient under consideration is associated, to a cell where the optimal solution in that cell attains its lower bound or its upper bound. The discussion relative to the case when the coefficient under consideration is associated to a cell in the optimal basis is given in two parts. The first part deals with the primal changes of the optimal solution while the second part is concerned with the dual changes. It is shown that the optimal cost varies in a nonlinear fashion when the coefficient changes linearly in certain cases. The discussion in this paper is limited to basis-preserving operators for which the changes in the data are such that the optimum bases are preserved. Relevant algorithms and illustrations are provided throughout the paper. 相似文献